• Communications for Statistical Applications and Methods
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• 제28권1호
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

• Journal of the Korean Data and Information Science Society
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• 제17권4호
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• pp.1397-1403
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• 2006

This paper considers the testing problem for scale changes in autoregressive processes with heavy-tailed innovations. For a test, we propose the CUSUM test statistic based on the trimmed residuals. We perform a simulation study for the mixture normal and Cauchy innovations.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 심포지엄 논문집 정보 및 제어부문
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• pp.18-20
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• 2006

The statistics for the neighbor differences between the particular pixels and their neighbors are introduced. They are incorporated into the filter to remove additive Gaussian noise contaminating images. The derived denoising method corresponds to the maximum likelihood estimator for the heavy-tailed Gaussian distribution. The error norm corresponding to our estimator from the robust statistics is equivalent to Huber's minimax norm. Our estimator is also optimal in the respect of maximizing the efficacy under the above noise environment.

• Communications for Statistical Applications and Methods
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• 제18권6호
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• pp.717-732
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• 2011

꼬리가 두꺼운 분포의 고분위수에 대한 신뢰구간을 구할 때 적절한 붓스트랩 방법은 무엇인가에 대해 알아보았다. 비모수적 방법과 모수적 방법, 그리고 준모수적 방법의 성능을 모의실험을 통해 비교하였다.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2010년도 추계학술대회
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• pp.35-39
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• 2010

The research classifies three types of asymptotic tail distributions such as long(heavy, thick) tailed distribution, medium tailed distribution and short(light, thin) tailed distribution. The extreme value distributions(EVD) classified in this paper can be used in SPC(Statistical Process Control) control chart and reliability engineering.

• 대한수학회지
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• 제61권5호
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• pp.853-874
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• 2024

Let {X, X_n; n ≥ 1} be a 𝛽-mixing sequence of identical nonnegative random variables with super-heavy tailed distributions and S_n = X₁ + X₂ + · · · + X_n. For 𝜀 > 0, b > 1 and appropriate values of x, we obtain the logarithmic asymptotics behaviors for the tail probabilities ℙ(S_n > e^𝜀nx) and P(S_n > e^𝜀bn). Moreover, our results are applied to the log-Pareto distribution and the distribution for the super-Petersburg game.

• Communications for Statistical Applications and Methods
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• 제3권3호
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• pp.225-233
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• 1996

In this paper, we propose Bayes estimators of the finite population mean based on heavy-tailed prior distributions using scale mixtures of normals. Also, the asymptotic optimality property of the proposed Bayes estimators is proved. A numerical example is provided to illustrate the results.

• Communications for Statistical Applications and Methods
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• 제18권6호
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• pp.733-739
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• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

• Journal of the Korean Data and Information Science Society
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• 제11권2호
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• pp.313-318
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• 2000

This article addresses aspects of combining information, with special attention to meta-analysis. In specific, we consider hierarchical Bayesian models for meta-analysis under priors which are scale mixtures of normal, and thus have tail heavier than that of the normal. Numerical methods of finding Bayes estimators under these heavy tailed prior are given, and are illustrated with an actual example.

• 정보처리학회논문지A
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• 제10A권3호
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• pp.189-198
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• 2003

본 논문에서는 TTT 타점법을 이용하여 웹 서버가 서비스하는 파일의 크기에 대한 통계적 분포는 꼬리부분이 두꺼운 분포라는 것을 판단하는 방법을 제시한다. TTT 타점법은 신뢰성 공학에서 사용되는 방법으로써 TTT 통계량 타점결과의 직선성으로 지수분포 여부를 판단하는 방법이다. 본 연구에서 제안하는 방법을 모의실험과 실제 운영중인 웹서버의 자료를 사용하여 실험한 결과, 기존의 방법인 Hill 추정법과 LLCD 타점법에 비하여 후미성을 정확하게 판단하고 있으며, 판단의 효율성 면에서도 그들보다 우수하다는 것을 확인하였다. 특히 제안하는 방법은 기존의 방법이 웹서버의 파일 분포판정이나 통계학에서의 파레토 분포 판정시 나타날 수 있는 판정의 오류 가능성을 개선할 수 있다는 점도 확인하였다.